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Math Help - Empty tank problem.

  1. #1
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    Empty tank problem.

    I'm not quite sure if this problem is pre-calculus, but there is no specified way to solve it, and it's giving me a lot of trouble.

    An empty tank with 1 gate at each end is filled and drained with water. You start a 20 second timer, and every 1.323 seconds after the timer is started gate 1 opens and shuts instantly letting in 150 L of water. Also every 2 seconds after the timer has been started gate 2 opens and shuts instantly letting 60 L of water out. After the 20 seconds has elasped, how much water has been drained from the tank, and how much is remaining in the tank?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jpatrie View Post
    I'm not quite sure if this problem is pre-calculus, but there is no specified way to solve it, and it's giving me a lot of trouble.

    An empty tank with 1 gate at each end is filled and drained with water. You start a 20 second timer, and every 1.323 seconds after the timer is started gate 1 opens and shuts instantly letting in 150 L of water. Also every 2 seconds after the timer has been started gate 2 opens and shuts instantly letting 60 L of water out. After the 20 seconds has elasped, how much water has been drained from the tank, and how much is remaining in the tank?
    Seems to me like we need to know the size of the tank.
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  3. #3
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    I think you're supposed to assume the tank's size doesn't matter, like every 1.323 seconds you transport 150 L of water to some point in space and 60 L is transported out every 2 seconds.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jpatrie View Post
    I think you're supposed to assume the tank's size doesn't matter, like every 1.323 seconds you transport 150 L of water to some point in space and 60 L is transported out every 2 seconds.
    OK. So, how would we discover at what time it would be empty if we don't know how big it is? Or anything about it at all for that matter. I could definitely tell you how much water was dispensed at any given time, but it is impossible to say when it will be empty. Perhaps you could report the problem as it is written, word-for-word.
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  5. #5
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    Quote Originally Posted by jpatrie View Post
    I'm not quite sure if this problem is pre-calculus, but there is no specified way to solve it, and it's giving me a lot of trouble.

    An empty tank with 1 gate at each end is filled and drained with water.
    I don't know what that means and I suspect that is the difficulty here. I am going to assume that does not mean "completely filled or completely drained", just that some water comes in and some goes out.

    You start a 20 second timer, and every 1.323 seconds after the timer is started gate 1 opens and shuts instantly letting in 150 L of water. Also every 2 seconds after the timer has been started gate 2 opens and shuts instantly letting 60 L of water out. After the 20 seconds has elasped, how much water has been drained from the tank, and how much is remaining in the tank?
    In 20 seconds there are 20/2= 10 2 second periods. However, you did not open the first gate at t=0 or at t= 20 so it has been opened 19 times, Multiply 19 times 60L to find how much water has been drained from the tank.

    The other gate opens every 1.323 seconds and 20/1.323= 15.11 so that gate has been opened 15 times. Multiply 15(150) to find how much water has gone into the tank. In order to say "how much is remaining in the tank", we would have to know how much water was in the tank at the beginning. I suspect it was intended that the tank be empty at the beginning.
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